a) Field of the Invention
This invention relates to a multilayer film reflecting mirror suitable to an optical element for use in an X-ray optical system.
b) Description of the Prior Art
Recently, attention has come to be attracted to an artificial grating, as a reflecting mirror for soft X rays, comprising thin films laminated with film thicknesses between several and several hundred angstroms. It is usual for the lamination technique of the artificial grating to alternately laminate the thin film of a substance A with a low refractive index and that of a substance B with a high refractive index, over the range of several tens of layers to several hundred layers, in a soft X-ray region. For instance, W (tungsten), Ni (nickel) or Mo (molybdenum) is known as the substance A, while C (carbon), B (boron), Be (beryllium) or Si (silicone) as the substance B [T. Namioka, Revue Phys. Appl., Vol. 23 (1988), pp. 1711-1726]. In the case where the substances A and B are alternately built up, various methods are known, for example, of laminating periodically individual substance layers whose film thicknesses are made constant and of laminating the film layers which are optimized for each layer [Takeshi Namioka et al., "Developments of Light Sources and Optical systems for Soft X-ray Lithography", Report of Research by Scientific Research-Aid Fund for the 1985 Fiscal Year (Test Research (2)), pp. 1-36, 1986]. Additionally, for the purpose of preventing individual substances from diffusing at the interface between the layers of the substances A and B, an artificial grating is also devised which comprises at least three kinds of substances by providing a buffer layer, between the layers of the substances A and B, constructed of other substance (U.S. Pat. No. 4,693,933). For a film fabrication, approaches, such as electronic beam evaporation, sputtering and laser beam techniques, are known and the examples of the artificial grating using these film fabrication techniques are also reviewed [H. Yamashita, O plus E, Feb., 1987, pp. 67-83; T. Namioka et al., Journal of the Japanese Society of Precision Engineering, Vol. 11 (1986), pp. 16-18]. To secure a sufficient reflectance in the soft X-ray region, however, a working technique with a high degree of accuracy is required and hence there is the report that a surface roughness of 1 nm or less is required for a substrate and that of 1.4 .ANG. or less for the interfaces between individual layers (U.S. Pat. No. 4,727,000).
Consideration is also given to theoretically design and evaluate the reflectance of the multilayer film reflecting mirror making use of the artificial grating mentioned above, and in general, when X rays in a long wavelength region are incident and in a grazing incidence region, the difference in reflectance between a design value and a measured value is small. In such instances, it is effective to apply Fresnel's recurrence formula as a theoretical model. FIG. 1 shows an optical model of the multilayer film reflecting mirror, in which reference symbol R.sub.m-1 represents the complex amplitude reflectance in the case where the substances are laminated to the (m-1)-th layer for film fabrication and N.sub.m-1 the complex index of refraction of the (m-1)-th layer. The complex amplitude reflectance in the case where the substance having a complex index of refraction N.sub.m is further laminated thereon, with a thickness of d.sub.m, is designated by R.sub.m, which is given by ##EQU2## where r.sub.m is the Fresnel coefficient relating to a vacuum of the m-th layer of a new lamination, .delta..sub.m is the phase difference between both ways in the m-th layer, and i is the unit of the imaginary number [T. Namioka, Revue Phys. Appl., Vol. 23 (1988), pp. 1711-1726]. For the p-polarized light component. ##EQU3## For the s-polarized light component, ##EQU4## where .phi. is the angle of incidence at which X rays are incident on the multilayer film through the vacuum and .phi..sub.m is the complex angle of refraction. Also, when the wavelength is taken as .lambda., the phase difference .delta..sub.m is given by ##EQU5##
If, therefore, the substrate not shown is taken as m=0 and Equation (1) is used, in turn, from the 0-th layer to the m-th layer to determine R.sub.m, a desired reflectance of the multilayer film reflecting mirror can be calculated.
FIG. 2 shows the design value and the measured value of the reflectance in the case where X rays with a wavelength of 1.5 .ANG. are incident while the angle of diffraction is made to change, on the multilayer film reflecting mirror comprising W of a film 17.3 .ANG. thick and C of a film 34.7 .ANG. thick, built on the substrate into 11 layers. In this case, as will be obvious from FIG. 2, the difference in reflectance between the design value and the measured value is extremely small. If, however, the wavelength of X rays to be incident is shorter or X rays enter at the normal incidence, the difference will become larger. This is attributed to two points indicated below.
(a) In the case of the incidence of X rays having a shorter wavelength or at the normal incidence, the film thickness per layer must be diminished. This makes it difficult to uniform the film thickness with the deterioration of reflectance.
(b) In the case of the incidence of X rays having a shorter wavelength or at the normal incidence, the interference condition of the X rays become severe, with the result that the roughness of each interface is more liable to affect the X rays.
Most of the multilayer film reflecting mirrors of the prior art mentioned above have been fabricated in view of the case where X rays are incident principally at a grazing angle of 20.degree. or less in the grazing incidence region or where X rays having long wavelengths of 100 .ANG. or more are incident in the normal incidence region. These mirrors can bring about the reflectance close to the design value if the roughness of the interface is sufficiently controlled. When X rays of short wavelengths are incident in the normal incidence region, however, problems are caused by the property of interference of X rays, due to the reasons of the above points (a) and (b), within the multilayer film reflecting mirror. In a multilayer film reflecting mirror illustrated in FIG. 3 which comprises the thin films of two kinds of substances A and B different in refractive index from each other, laminated alternately with the thicknesses of d.sub.1 and d.sub.2, respectively, when the thickness of a pair of layers (which will be hereinafter referred to as periodic thickness) is represented by d, the wavelength of an X ray by .lambda., and the grazing angle by .theta., Bragg's condition becomes EQU 2d sin .theta.=.lambda. (5)
and the periodic thickness d is expressed by ##EQU6## In other words, the periodic thickness reduces as the wavelength .lambda. becomes short and the incident angle is small. Consequently, incident X rays interfere within the multilayer film reflecting mirror, so that the highest reflectance needs to control correctly the thickness of the multilayer film with the accuracy corresponding to the periodic thickness d.
In the above case, however, no discussion is made in detail as to how the accuracy of the film thickness should be controlled under any condition. FIG. 4 depicts the design example of the multilayer film reflecting mirror comprising Ni and Sc built up of 201 layers, with the film thicknesses of 8.2 .ANG. and 11.8 .ANG., respectively. It is constructed so that when the reflecting mirror is fabricated, an actual film thickness generally have a tolerance .DELTA.d with respect to the design value of each film thickness. The tolerance .DELTA.d may be assumed to arise at random in the probability according to the normal distribution given by ##EQU7## where .sigma. is the deviation. According to Equation (7), the value of .DELTA.d of -.sigma..ltoreq..DELTA.d.ltoreq..sigma. appears in the probability of 68%. FIG. 5 shows the results of simulation of the reflectances in the cases where X rays having a wavelength of 39.8 .ANG. are incident while the incident angle is made to change, on the multilayer film reflecting mirror fabricated so that the film thickness has the tolerance .DELTA.d for the design value and where the deviation .sigma., that is, the accuracy of the film fabrication is changed. According to FIG. 5, as the deviation .sigma. increases from 0 .ANG. to 0.4 .ANG., the reflectance materially reduces, and consequently, there is the feasibility that even the reflecting mirror fabricated with a deviation of about 0.4 .ANG. cannot be utilized as a useful one. In the case where, as mentioned above, the film thickness deviates at random from the design value in accordance with the normal distribution, some multilayer film reflecting mirrors fabricated will exhibit remarkably low reflectances in view of the theory of probability. Thus, the multilayer film reflecting mirrors of the prior art in practical fabrication have been difficult to bring about the stabilization of their qualities and the improvement in a product yield.